\int_{k}^{\infty} e^{-a^{2}} dy (gauss int. w. finite lim.)

I am doing a calculation of overlap between wavefunctions in a physics thesis, however this integral puzzles me:

$\displaystyle \int_{-L/2+\kappa a^{2}}^{\infty} e^{-\frac{1}{2a^{2}}y^{2}} dy$

From a physic point of view it is very important that the integral is from $\displaystyle -L/2+\kappa a^{2}$ and not from $\displaystyle -\infty$. I am awere that is is impossible to write down an antiderivative of the function being integrated however, there must be some way to deal with the integral.

How do I calculate this integral (as a function of momentum $\displaystyle \kappa$)?